FOURIER ANALYSIS: The Fourier integral of a Lebesgue integrable function is statistically convergent
almost everywhere to the given function. The maximal Fejér operator applied to any integrable function $f$ is in $L^1$ if and only if $f$ is in the real Hardy space $H^1$. The maximal conjugate and Hilbert operators are not bounded from the real Hardy space $H^1$ to the space $L^1$. A number of theorems of R.P. Boas on the interrelation of absolutely convergent sine and cosine series with nonnegative coefficients and classical function classes were generalized for arbitrary absolutely convergent Fourier series.
FUNCTIONAL ANALYSIS: The classical monotone convergence theorem of Beppo Levi fails in
noncommutative $L_2$-spaces.
APPROXIMATION THEORY: A theorem of L. Leindler on the interrelation between the generalized
Zygmund classes $\Omega_\alpha$ of functions and strong approximation by Fourier series was
extended from $\alpha=1$ to $0